Metric-independence of vacuum and force-free electromagnetic fields

Understand

Electromagnetic fields which solve the vacuum Maxwell equations in one spacetime are well-known to also be solutions in all spacetimes with conformally-related metrics.

• This provides a sense in which electromagnetism alone cannot be used to measure certain aspects of geometry.
• We show that there is actually much more which cannot be so measured; relatively little of a spacetime's geometry is in fact imprinted in any particular electromagnetic field.
• This is demonstrated by finding a much larger class of metric transformations---involving five free functions---which preserve Maxwell solutions both in vacuum, without local currents, and also for the force-free electrodynamics associated with a tenuous plasma.